Here,
\(r(t) \equiv \sqrt{\Gamma } R_e(t) e^{i \delta _a^{ (0) } t}\) 
and
\(f(t) \equiv i\sqrt{\Delta }\exp [-(\Delta /2 + i\omega _L)t]\) .
This approximately linear dependence is obtained from Eq.(REF ), which depends on the entire history of the photon pulse, revealing the non-Markovianity of the dynamics of the lambda systems [1]}.
In the monochromatic regime, however, we find that Eq.(REF ) holds at times \(t\gg \Gamma ^{-1}\) .
By writing the susceptibility in terms of its real and imaginary parts,
\(\chi = \chi ^{\prime } + i \chi ^{\prime \prime },\) 
